Question

A car moving with a speed of 72kmph towards a hill. Car blows horn at a distance of $1800m$ from the hill. If the echo is heard after $10s$, the speed of sound (in $m/s$) is
(A) $300$
(B) $320$
(C) $340$
(D) $360$

Answer 1

For solving this question, we have to calculate the total distance covered by the sound in its whole journey of reaching the hill and returning back. Then, by using the basic formula of speed, we will get the required speed.

Complete step by step solution:
Let the speed of sound be equal to $v$
Let $t = 0$ be the time when the car blows a horn.
According to the question, at this time the car is at a distance of $1800m$ from the hill.
Therefore, the distance covered by the sound to reach the hill from the car
$\Rightarrow{d_1} = 1800m$ ……………………….(i)
Now, for hearing the echo, the sound must return back to the car. But in the meanwhile, the car is moving towards the hill. So, the returning distance for the sound will be less than the original distance of $1800m$.
The speed of the car
$\Rightarrow u = 72km/h$
$\Rightarrow u = 72 \times \dfrac{{1000m}}{{60 \times 60s}}$
On solving, we get
$\Rightarrow u = 20m/s$
The echo is heard after $t = 10s$. So, the distance covered by the car during this time is
$\Rightarrow x = 20 \times 10$
$\Rightarrow x = 200m$
So, the distance of the car from the hill
$\Rightarrow {d_2} = {d_1} - x$
$\Rightarrow {d_2} = 1800 - 200 = 1600m$ ……………………….(ii)
So, this is the distance which is to be covered by the sound to return to the car.
Total distance covered by the sound
$\Rightarrow d = {d_1} + {d_2}$
From (i) and (ii)
$\Rightarrow d = 1800 + 1600$
$\Rightarrow d = 3400m$
Now, we know that the speed is equal to the total distance covered divided by the total time. So we have
$\Rightarrow v = \dfrac{d}{t}$
$\Rightarrow v = \dfrac{{3400}}{{10}}$
On dividing, we finally get
$\Rightarrow v = 340m/s$
Thus, the speed of sound comes out to be equal to $340m/s$.

Hence, the correct answer is option (C).

Note:
Do not make the mistake of taking the total distance covered by the sound equal to twice the original distance. As the car and the sound are simultaneously travelling, so we have to divide the journey of the sound into two parts. One in which the sound reaches the mountain, and the other in which the sound returns back.
Also, remember to convert the values given into SI units. The speed of the car in this question was not in the SI units.